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Abstract

In this paper we studied the effects of external fields' polarization on the coupling
of pure magnetic fields into human body. Finite Difference Time Domain (FDTD) method
is used to calculate the current densities induced in a 1 cm resolution anatomically
based model with proper tissue conductivities. Twenty different tissues have been
considered in this investigation and scaled FDTD technique is used to convert the
results of computer code run in 15 MHz to low frequencies which are encountered in
the vicinity of industrial induction heating and melting devices. It has been found
that external magnetic field's orientation due to human body has a pronounced impact
on the level of induced currents in different body tissues. This may potentially help
developing protecting strategies to mitigate the situations in which workers are exposed
to high levels of external magnetic radiation.

Background

Coupling of external electromagnetic fields into the human body has been subject of
many investigations in recent years especially with several epidemiological studies
linking higher rates of incidence of certain cancers with electromagnetic radiation
[1,2]. Many investigations have been made to evaluate EM waves coupling into different
organs of body and many international guidelines and standards have been set up for
exposure limits in order to protect workers against nonionizing radiation in their
workplaces.

Regarding the fact that many cancer associations have referred to magnetic radiation
and considering the fact that magnetic fields are not shielded by conventional shielding
structures, has led to a dominant interest in exploring potential hazards of magnetic
induction.

There are many studies in recent years evaluating levels of current densities induced
in different body tissues when exposed to low frequency EM waves. The well known scaled
FDTD technique has been used widely since proposed by Gandhi [3-5] to convert the results of a simulation performed in a higher frequency (in the range
of mega hertz) to the results of very low frequency coupling caused by power line
radiation in 50 and 60 Hz. Other studies considering the effects of uniform and nonuniform
magnetic fields with various polarizations are also performed at 60 Hz using quasi-static
impedance method [6].

Different combinations of incident waves, including pure magnetic fields with different
polarizations and both electric and magnetic fields in the form of a uniform plane
wave have been studied in Gandhi's works at power line frequencies. Other studies
have explored effects of very low frequency pure electric fields using high resolution
models (with cubic voxels of 3.6 mm edges) [6]. Industrial frequencies in the range of kilo hertz have been also studied due to
potential risks imposed on workers near induction heating and melting devices and
it has also been shown that for low frequency dosimetric applications, using 1 cm
resolution model with realistic shape but relatively lower resolution in discrimination
of internal tissues may give good results with acceptable accuracy [7].

In this paper a 1 cm resolution anatomically based model with 20 different organs/tissues
has been used to evaluate current densities induced in different parts of body when
exposed to pure magnetic fields in frequency of 1 KHz. This particular frequency is
of interest for two major reasons: first, this is the frequency mostly radiated by
industrial heating and melting devices in work places for which many basic restrictions
indicating the maximum permissible values of electric and magnetic field inside the
human body have already been established. The second, this is the frequency proven
to have a remarkable impact on the phenomenon of cell electroporation [8,9]. In this phenomenon, tiny pores will be formed on the membrane of cells exposed to
electric fields with a particular frequency and magnitude. These pores are formed
in several microseconds and may last up to some seconds and the process is irreversible
if the voltage induced on the cell membrane exceeds a critical value and cell death
will occur. Therefore, studying the magnitude of induced electric fields in different
body tissues may potentially help obtaining a better control and insight into potential
occurrence of electroporation phenomenon.

The model is manually prepared by converting MRI images of a 46-year old man with
the height of 178 cm into suitable matrixes of electrical properties of computational
space to be used in FDTD algorithm. MRI images were T1-weighted and obtained with
a 1.5T unit and the following parameters: TR = 300–450 ms, TE = 12–15 ms, matrix size
= 256 × 256.

20 different tissues and related organs have been identified by an expert physician
and a consulting radiologist and have been discriminated due to variations in their
conductivities. Pure magnetic radiation is simulated using two plane waves traveling
in opposite directions with electric components canceling each other.

It is shown that the orientation of magnetic vector in respect with the body may have
a considerable impact on the coupling of external fields into different organs. This
may be useful to be considered when seeking for appropriate protective strategies
against unwanted effects of external radiation.

FDTD algorithm and human body modeling

The anatomic based human body model used in our work has been prepared manually using
data from MRI images of a 46-year old man with the height of 178 cm. These images
have been then converted to thee dimensional matrixes introducing electrical properties
of human body to the computational environment in FDTD algorithm. Fig. 1 shows some sensitive organs included in the model. Related conductivities for different
parts of body are obtained from [10] for the frequency of 1 KHz.

Figure 1. Views of anatomic model of human body used in the simulation.

The whole FDTD computational space has been divided into 80 × 80 × 200 = 1280000 cubic
cells with the cell size of 1 cm. The human body is suspended in the air and the computational
space is terminated to a 10-layer PML (Perfectly Matched Layer) with a grading profile
and the optimum conductivity as described in [11].

To simulate the interaction of low frequency incident waves with human body, scaled
FDTD method is used as described in [4]. According to Gandhi, in this case the electric fields outside the body depend not
on the internal tissue properties, but only on the shape of the body as long as the
quasi-static approximation is valid, i.e., the size of the body is a factor of 10
or more smaller the wavelength, and |σ + jωε| >> ωε0 where σ and ε are the conductivity and permittivity of the tissues, respectively. Under these conditions
electric fields in air are normal to the body surface and the internal electric fields
are given from the boundary conditions in terms of the fields outside:

(1)

A higher quasi-static frequency of f' maybe therefore used for irradiation of the model and the induced electric fields
E' thus calculated may be scaled back to the frequency of interest f.

From the equation (1) we can write:

(2)

Assuming that σ + jωε ≅ σ at both f and f'

In many cases if σ' and σ are close enough we can simplify the equation (2) to

(3)

In our program the actual FDTD program is performed at a frequency of f' = 15 MHz and afterwards the induced electric field E' in the frequency of f' is scaled to the frequency of interest f using equation (3). As it is obvious from (2) the permittivity of tissues doesn't
affect the results significantly, therefore the value of εr = 1 has been set for the whole environment to hasten the speed of wave propagation.

In order to generate a homogeneous magnetic field the model is exited simultaneously
by two plane waves traveling in opposite directions. With the appropriate orientation
of plane waves electric field components cancel out and the magnetic components superpose
constructively. Two different orientations for magnetic field vector are studied:
front to back and foot to head and the magnitude of electric field of each plane wave
is 100 V/m.

The total average electric current for different layers of body height is obtained
from the equation (4). When FDTD runs, the magnitude of electric fields inside the
body reaches an overshoot during the beginning time steps and then follows a sinusoidal
pattern with lower amplitude. This overshoot has not been considered when calculating
the temporal maximum of currents. To calculate the average of total electric current
for each layer we have simply added elemental currents of each cell in the layer and
divided the result by the number of contributing cells.

(4)

Numerical results

Fig. 2 shows the layer-averaged induced currents computed for two different polarizations
of magnetic field. It is obvious that orientation of the body with respect to external
fields has a pronounced impact on the coupling of fields into body.

Figure 2. Layer-averaged electric current for two different polarizations of magnetic field.

For different organs, the organ-averaged electric current has been also calculated
for two magnetic field's polarizations. Fig. 3 shows the results of this calculation. It is observed that for most of organs the
front to back magnetic vector orientation has more powerful coupling effects than
side to side magnetic vector, though this trend is reversed for some specific parts
of body. In [4] also, different orientations of fields due to human body are studied for 60 Hz pure
magnetic fields, but the results do not show such pronounced differences between curves
of layer averaged electric currents. This may be because of the fact that in [4] a more homogeneous human model is used and less discrete tissue/organs are considered.

Figure 3. Organ-averaged electric current for different parts of body.

The differences are more pronounced for some specific organs like thymus and thyroid
glands. If it is clinically proven that electric currents may some how affect the
function of these organs, then the results obtained from this study may help suggesting
some mitigating techniques to reduce the potential hazardous effects of unwanted external
radiation, i.e. by setting some restrictions on workers orientations due to industrial
devices.

To verify the model, the results are compared with the results presented in [7]. In this work, a pure magnetic field with the vector oriented from front to back
of the body is simulated to produce B = 30.7 μT. The electric field of each of the two plane waves must therefore be 0.92 V/m. Fig.
4 shows the maximum of electric current induced in different body parts. If we scale
the results presented in Fig. 4 by dividing them to the scale factor 1087, they will show a good agreement with results
presented in [7]. Slight differences between results may be due to differences in weight and height
of actual models.

Figure 4. Maximum of total electric current for different parts of body.

Conclusion

In this work the effects of external magnetic fields' orientation on the coupling
of fields into human body in very low frequencies have been studied using an inhomogeneous
anatomic human model. It has been shown that the coupling of external fields into
different organs and tissues may be affected considerably by changing the orientation
of external filed vectors. This effect is more pronounced for some specific organs
like thyroid and thymus gland and calls for further studies on potential effects of
electric currents on function of these organs.